Highly-Efficient Local Proofs and Codes (Invited Talk)

Abstract

Interactive oracle proofs (IOPs) extend the classical notion of probabilistically-checkable proofs (PCPs) by allowing a verifier to interact with a prover over a small number of rounds, while querying the prover’s messages in only a few locations. 
A recent line of work gave highly-efficient IOPs outperforming state-of-the-art PCPs, for example, constant-round and constant-query (ZK-)IOPs with only a linear (and even approaching the witness length) amount of communication, as well as (ZK-)IOPs with linear-time prover complexity. These constructions were leveraged in turn to obtain highly-efficient succinct arguments and zero-knowledge proofs. 
The improved efficiency was obtained by replacing polynomial-based codes, commonly used in such proof systems, with more efficient (tensor-based) codes. In particular, these constructions bypassed a barrier imposed by the need to encode the computation using a multiplication code. 
In the talk I will survey these highly-efficient IOP constructions, and highlight some interesting open problems raised by these works.